All Answers 358087 Answers

Thanks Alan but I'm really not concerned.  

If I were one of the children that would definitely be true.

But I'm not and it just doesn't matter. 

Option2 : Renting

Rent = 550*52*3 = $85800

$$\begin{array}{rll}
Future \;Value\; of \;term\; deposit&=&P(1+i)^n\\\\
&=&112000(1+0.0525/12)^{36}\\\\
&=&\$131,060\\\\
\end{array}$$

Renting Balance after 3 years = 131,060-85800= $45,260

Buying Balance after 3 years = $168,923-$12000 = $156,923

Well, buying appears to be the better option.

I am surprised I will admit, I didn't think the difference wouldbe this great.  

Option 1 :  Buying

cost = $560,615.26   I'll round off to $560,615

Deposit = 0.20*$560615 = $112,123 = $112,000  (roounded to the nearest thousand - paid in cash)

A= Amount borrowed = $560615 - $112000 = $448,615

Interest on loan = 6.5%pa = 0.065pa :

i = 0.065/12 = 0.0051666666666 per month

R = Regular payment = $3032.80 per month

The time to repay the loan n  must be determined. 

$$\boxed{ \mbox{Present value of an ordinary annuity }\qquad
A=R\times\frac{1-(1+i)^{-n}}{i}}$$

$$\begin{array}{rll}
A&=&R\times\frac{1-(1+i)^{-n}}{i}\\\\
448615&=&3032.80\times\frac{1-1.005416666666666^{-n}}{0.005416666666666}\\\\
\frac{448615\times 0.005416666666666}{3032.80}&=& 1-1.00516666666666^{-n}\\\\
\dfrac{448615\times 0.005416666666666}{3032.80}-1&=& -1.00516666666666^{-n}\\\\
-0.198760908&=& -1.005416666666666^{-n}\\\\
0.198760908&=& 1.005416666666666^{-n}\\\\
log(0.198760908)&=& log(1.005416666666666^{-n})\\\\
log(0.198760908)&=& -n*log(1.005416666666666)\\\\
\frac{log(0.198760908)}{log(1.005416666666666)}&=&-n\\\\
n&=&\frac{-log(0.198760908)}{log(1.005416666666666)} \\\\
n&=&299.08\;months \\\\
Loan\; period&=&25\;years\\
\end{array}$$

So now you need to go backwards to work out how much is owing on the house after 3 years.

22 years of the loan is left = 22*12 = 264 months

$$\begin{array}{rll}
A&=&R\times\frac{1-(1+i)^{-n}}{i}\\\\
A&=&3032.80\times\frac{1-(1.00541666666666)^{-264}}{0.00541666666666}\\\\
A&=&\$425,394\\\\
\end{array}$$

Equity after 3 years without considering appreciation = $560,651 - $425,394 = $135,221

Equity after 3 years considering appreciation = $135,221 * 1.077³ = $168,923

Costs without any adjustments = $12000

Balance after 3 years = $168,923-$12000 = $156,923

I can't understand why you put it 

 (2x - 3) and (3x + 2)

With real numbers you cannot have the logarithm of a negative number.

With complex numbers

$$\log_2{(-m)}= \log_2{(m)}+\frac{(2n+1)\pi}{\ln2}*i$$ 

where m is positive and n is any (positive or negative) integer.

1st question

Sorry, the 20% is not 461,000 that was for a different house that I had to do!, the 20% is $448,492.208 which then I would need to have rounded up to $449,000 so its per thousand which was for my other questions. 

2nd question 

Yes interest is charged at 6.5% p.a 

Option 2 question 

Oh thank you, I was not sure what Formula would be needed to solve/find the answer to option 2 (dot point 2) 

$$\frac{2}{5}\times\frac{3}{7}=\frac{2\times3}{5\times7}=\frac{6}{35}$$

In approximate decimal representation:

$${\frac{{\mathtt{6}}}{{\mathtt{35}}}} = {\mathtt{0.171\: \!428\: \!571\: \!428\: \!571\: \!4}}$$

I have a couple of questions of my own in the buying options and I have given you a pointer in the renting option.

--------------------

**You need to work out what the two values-costs are at the end of 3 years.

**This can be done with different degrees on complexity depending on what level you are studying at.

Option 1:Buying a property considering:

• you purchase the property you have chosen ($560,615.26)
• you have your 20% deposit saved ($461,000.00)

Q: Where did $461,000.00 come from??  It is not 20% or 80% of $560615.26

• you make your regular monthly repayments (3032.80) – 6.5%

Q: Is interest charged at 6.5% p.a. ??

• house maintenance expenses are approximately $4 000 a year (haven’t factored)
• property values appreciate by 7.7% per annum. (Haven’t factored)

Option 2: Renting over a period of three years considering:

• You rent a similar property to the one you have chosen. As a general rule, weekly rent payments would be equal to $1 for every $1 000 of the value of the home. (value of home is $550,000 so $550)
• The deposit you have saved (same as in Option 1) will be invested into a term deposit for the three years at 5.25% per annum, compounding monthly (Haven’t done)

How much will the deposit grow to after three years if it is just invested??  This is just a compound interest amount  FV=P(1+r)^n

1. Try adding up, say, 127 three hundred and eighty nine times.

2. Try adding up 8 one seventh times. 

3. Try calculating 7! (that's 7 factorial = 7*6*5*4*3*2*1) using repeated addition.

Try these and you'll quickly come to appreciate multiplication!

What I mean is that the $1 every week for rent whichwould equivelate to $550 rent per week 

Ive worked out most of the calculations. Pretty much anything in brackets next to the dot points I have worked out but I need help with factoring in the last two dot points of option 1 and I am struggling to work out the last dot point in option 2, I dont mean to ask for you to do it, I meant help, im sorry 

Just the one!

If t_n = n-1 then t₉₉ = 98,  t₁₀₀ = 99 (= t₉₉ + 1) and t₁₁ = 10 so that t₁₁² - 1 = 99 (= t₁₀₀)

There are an infinite number of functions that would satisfy this!  I think the question is incomplete.

However, the process is more important than the result here, so, although you might not get full marks you should get some for showing the correct way of doing it!

a) Presumably the customer paid $120

b) If it was discounted by 20% then this is 80% (or 0.8) of its original price, so 0.8*original price = $120

Divide both sides by 0.8 to get original price = $150

Thanks Dragon but it doesn't matter.

We should all get negative points sometimes.  

It reminds us to be careful and also to behave appropriately.  

That is excellent Dragon.   

$$\begin{array}{rll}
S&=&(10-2)180\\
S&=&(10-2)\times 180\\
S&=&8\times 180\\
S&=&1440 \qquad \qquad \mbox{OR}\\\\
S&=&(10-2)180\\
S&=&10*180-2*180\\
S&=&1800-360\\
S&=&1440\\
\end{array}\\$$

Well I am very impressed !!

I am going to give you 3 points just for your brilliant LaTex   

Yes. I did it by myself. It was pretty easy. I have to write \pi so $$\pi$$ could appear.

And with the basic knowledge that I have learned, yes. It helped me a lot.

$$\mbox{This\;is\;just\;an\;example.}\\\\n^\infty\\\\=2^\infty\\\\=\infty$$

Great answer, Melody. I didn't know that. This is my basic knowledge.

But, thanks, Melody!

(Learned something new!)

I'll just add to Ninja's answer.

I think that a minus number raised to infinity would be undefined.

A positive number between 0 and 1 raised to infinity would be 0

A positive number greater than 1 raised to infinity would be infinity

Here is a graph.

Did you work out that LaTex code by yourself Dragon ??  I haven't seen you do anything like that before. 

You are not supposed to ask us to "do it"

You are supposed to ask us to 'help you'

How much have you done for yourself.  There as many aspects to this problem.